What is the minimum area of quadrilateral ABCD, if the area of a pair of diagonally opposite triangles (Formed by joining the diagonals of the quadrilateral) is 12 and 27 respectively?

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Solution

The correct option is C 75
Option c

In a quadrilateral, product of area of diagonally opposite triangles is same.

So, the product of other set of opposite triangles will be 1227

Now, we have to find minimum a and b such that ab=1227 and a+b is minimum.

So a = b = 18 (as 1227 = 324)

Hence the area of the quadrilateral = 18 + 18 + 12 + 27 = 75

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